Quantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum

Consider the family of Schr\"odinger operators (and also its Dirac version) on $\ell^2(\mathbb{Z})$ or $\ell^2(\mathbb{N})$ $$H^W_{\omega,S}=\Delta + \lambda F(S^n\omega) + W, \quad \omega\in\Omega,$$ where $S$ is a transformation on (compact metric) $\Omega$, $F$ a real Lipschitz function and $W$ a (sufficiently fast) power-decaying perturbation. Under certain conditions it is shown that $H^W_{\omega,S}$ presents quasi-ballistic dynamics for $\omega$ in a dense $G_{\delta}$ set. Applications include potentials generated by rotations of the torus with analytic condition on $F$, doubling map, Axiom A dynamical systems and the Anderson model. If $W$ is a rank one perturbation, examples of $H^W_{\omega,S}$ with quasi-ballistic dynamics and point spectrum are also presented.Comment: 17 pages; to appear in Journal of Differential Equation

Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator

An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schr?odinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case presents absence of dynamical localization for specific values of the energy, albeit it has no continuous spectrum. For the other energy values (again excluding some very specific ones) the Bernoulli Dirac system is localized, independently of the mass.Comment: 9 pages, no figures - J. Physics A: Math. Ge

Dynamical Lower Bounds for 1D Dirac Operators

Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to the discrete case, critical energies are also found for the continuous Dirac case with positive mass.Comment: 18 pages; to appear in Math.

Lactobacillus crispatus as the etiological agent in cytolytic vaginosis

Introduction: Lactobacillus spp. dominate the vaginal niche but can also be involved in other vaginal dysbiosis, such as cytolytic vaginosis (CV), which remains poorly studied. It is characterized by a cryptic symptomatology, that often confounds the clinic. Goals: The aim of this work was to search for the etiological agent of CV, by studying the vaginal microbiome and metabolomics of women afflicted with this disease and compare it with women with other clinical diagnostic. Methods: Twenty-one vaginal washes have been collected from women attending a gynaecology consultation of a private clinic. The samples were categorized according with clinical diagnosis at the time of sampling (CV, 11; vulvovaginal candidosis, 8; Healthy, 2). The distribution of bacterial species, and their prevalence was assessed by next-generation sequencing of the 16S V4 region. In addition, total lactate D-lactic acid and L-lactic acid was quantified in all washes by a commercial kit, as well as lactate dehydrogenase (LDH) activity. Results: L. crispatus was dominant (>70%) in all CV samples. Lactate was increased in CV in comparison with other cases. The presence of D-lactic acid isomer was associated with presence of L. crispatus. LDH activity was increased in vaginal washes that tested positive for the presence of L. crispatus, however no direct association was found with CV cases. Discussion/Conclusions: The microbiome of women afflicted with CV was dominated in all cases by L. crispatus, contrarily with the results obtained for women diagnosed with other clinical symptomatology. In addition, the finding that an increase in D-lactic acid is associated with CV patients can be related to the role of L. crispatus in CV. The determination of LDH activity did not correlate exclusively with CV cases. On the other hand, D-lactic acid and total lactate quantification could be used as a valuable biomarker to diagnose this cryptic vaginal infection.info:eu-repo/semantics/publishedVersio